Question

3x+2y+4z=12 X+y+2z=6 (X=0,y=4,z=1) Determine if the given 2 lines intersect at the given point. Explain your reasoning. -2x-4y+z=8 4x+2y=-5 (x=-2,y=0,z=3) same as up above

Answer 1

Equation 1: 3x + 2y + 4z = 12
Equation 2: x + y + 2z = 6

Substituting x = 0, y = 4 and z = 1 into equation 1 and equation 2 and if the answer equals to 12 and 6 then the two lines intersect at the given point

Equation 1 ⇒ 3(0) + 2(4) + 4(1) = 0 + 8 + 4 =12
Equation 2 ⇒ 0 + 4 + 2(1) = 4 + 2 = 6

We have the answer of 12 and 6, hence the two lines intersect at the given point
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Equation 1: -2x - 4y + z = 8
Equation 2: 4x + 2y = -5

Given point: x = -2, y = 0, and z = 3

Equation 1 ⇒ -2(-2) - 4(0) + 3 = 4 - 0 +3 = 7
Equation 2 ⇒ 4(-2) + 2(0) = -8 + 0 = -8

The answers are not 8 and -5 hence the lines don't intersect at given point